Abstract
SUMMARYHigh‐order accurate methods for convection‐dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy. The state of the art in this field is more advanced for Eulerian methods than for semi‐Lagrangian (SLAG) methods. In this paper, we introduce a new SLAG method that is based on combining the modified method of characteristics with a high‐order interpolating procedure. The method employs the finite element method on triangular meshes for the spatial discretization. An L2 interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes. Numerical results are illustrated for a linear advection–diffusion equation with known analytical solution and for the viscous Burgers’ equation. The computed results support our expectations for a robust and highly accurate finite element SLAG method. Copyright © 2012 John Wiley & Sons, Ltd.
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